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Greece National Olympiad
2015 Greece National Olympiad
1
1
Part of
2015 Greece National Olympiad
Problems
(1)
Equation with integers and prime
Source: Greek National MO 2015
3/4/2015
Find all triplets
(
x
,
y
,
p
)
(x,y,p)
(
x
,
y
,
p
)
of positive integers such that
p
p
p
be a prime number and
x
y
3
x
+
y
=
p
\frac{xy^3}{x+y}=p
x
+
y
x
y
3
=
p
number theory
prime numbers
Diophantine Equations